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Q.

Let [x] denote the greatest integer less than or equal to x. If x = (3+1)5 then [x] is equal to

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a

75

b

50

c

76

d

152

answer is D.

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Detailed Solution

x=(3+1)5=(3)5+5C1(3)4+5C2(3)3 +5C3(3)2+5C4(3)+5C5 =93+45+303+30+53+1=76+443∴ [x]=(3+1)5=(76+443)=(76)+(44×1.732)=76+(76.2)=76+76=152
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Let [x] denote the greatest integer less than or equal to x. If x = (3+1)5 then [x] is equal to